Consider the experiment of tossing a coin. If the coin shows head toss it again if it shows tail then throw a die. Find the conditional probability of the event the die shows a number greater than 4 given that there at least one tail.

Explanation

The sample space of an experiment that there is at least one tail and the die is thrown can be given as,

`S=(H,H),(H,T),(T,1),(T,2)(T,3)(T,4)(T,5)(T,6)`

Where `(T,i)` denotes that the first toss resulted in a tail and the number `i` appeared on the die for `i=1,2,3,4,5,6`.

Now, the probabilities of the above mentioned `8` elementary events are `1/4,1/4,1/12,1/12,1/12,1/12,1/12,1/12` respectively.

Now, let the event that 'there is at least one tail' be represented by `A` and the event 'the die shows a number greater than 4' be represented by `B`. Then,

`A=(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)`

And, `B=(T,5),(T,6)`

So, `AnnB=(T,5),(T,6)`

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